Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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        <div xml:id="echoid-div84" type="section" level="1" n="51">
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            <s xml:id="echoid-s743" xml:space="preserve">
              <pb o="21" file="033" n="33" rhead=""/>
            lum _B D,_ ponitur ſecare ad angulos rectos, erit ex defin. </s>
            <s xml:id="echoid-s744" xml:space="preserve">4. </s>
            <s xml:id="echoid-s745" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s746" xml:space="preserve">11. </s>
            <s xml:id="echoid-s747" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s748" xml:space="preserve">_E A,_ ad pla
              <lb/>
            num circuli _B D,_ recta; </s>
            <s xml:id="echoid-s749" xml:space="preserve">ac proinde cum ex E, centro ipſius educatur, in vtrunque
              <lb/>
            polum eiuſdem cadet. </s>
            <s xml:id="echoid-s750" xml:space="preserve">Cadit autem in circunferentiam circuli _A B C D,_ in ſuperficie
              <lb/>
              <note position="right" xlink:label="note-033-01" xlink:href="note-033-01a" xml:space="preserve">Schol. 8.
                <lb/>
              huius.</note>
            ſphæræ exiſtem ad puncta _A, C._ </s>
            <s xml:id="echoid-s751" xml:space="preserve">Sunt ergo _A, C,_ poli circuli _BD;_ </s>
            <s xml:id="echoid-s752" xml:space="preserve">at que adeo cir
              <lb/>
            culus _A B C D,_ circulũ _B D,_ per polos _A, C,_ ſecat. </s>
            <s xml:id="echoid-s753" xml:space="preserve">Quare ex præcedenti theoremate,
              <lb/>
            maximus circulus eſt. </s>
            <s xml:id="echoid-s754" xml:space="preserve">Probatum autem eſt, quod & </s>
            <s xml:id="echoid-s755" xml:space="preserve">circulum _B D,_ per polos ſecat.
              <lb/>
            </s>
            <s xml:id="echoid-s756" xml:space="preserve">Conſtat ergo propoſitum.</s>
            <s xml:id="echoid-s757" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div87" type="section" level="1" n="52">
          <head xml:id="echoid-head63" xml:space="preserve">IIII.</head>
          <p>
            <s xml:id="echoid-s758" xml:space="preserve">SI in ſphæra ſit circulus, & </s>
            <s xml:id="echoid-s759" xml:space="preserve">ab altero polorum eius recta cadens
              <lb/>
              <note position="right" xlink:label="note-033-02" xlink:href="note-033-02a" xml:space="preserve">24.</note>
            in planum ipſius ad angulos rectos æqualis ſit ſemidiametro eius,
              <lb/>
            circulus maximus eſt.</s>
            <s xml:id="echoid-s760" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s761" xml:space="preserve">_IN_ſphæra ſit circulus _AB_, à cuius altero polorum _C,_ in planum eius cadens re
              <lb/>
            eta perpendicularis _C D,_ æqualis ſit ipſius ſemidiametro. </s>
            <s xml:id="echoid-s762" xml:space="preserve">_Dico A B,_ eſſe circulum ma
              <lb/>
            ximum. </s>
            <s xml:id="echoid-s763" xml:space="preserve">Cum enim _C D,_ perpendicularis ſit ad circulum _A B,_ cadet ipſa in circuli
              <lb/>
            centrum, & </s>
            <s xml:id="echoid-s764" xml:space="preserve">producta cadet in alterum polum, qui ſit E. </s>
            <s xml:id="echoid-s765" xml:space="preserve">Eſt ergo _D,_ centrum circu
              <lb/>
              <figure xlink:label="fig-033-01" xlink:href="fig-033-01a" number="30">
                <image file="033-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/033-01"/>
              </figure>
              <note position="right" xlink:label="note-033-03" xlink:href="note-033-03a" xml:space="preserve">9. huius.</note>
            li _AB;_ </s>
            <s xml:id="echoid-s766" xml:space="preserve">atque adeo perpendicularis _C D,_ tran-
              <lb/>
            ſit per centrum ſphæræ. </s>
            <s xml:id="echoid-s767" xml:space="preserve">Ducatur per rectã _C E,_
              <lb/>
              <note position="right" xlink:label="note-033-04" xlink:href="note-033-04a" xml:space="preserve">Coroll. 2.
                <lb/>
              huius.</note>
            in ſphæra planum vtcunque faciens in ſphæra
              <lb/>
            circulum _A E B C,_ qui cum tranſeat per centrũ,
              <lb/>
              <note position="right" xlink:label="note-033-05" xlink:href="note-033-05a" xml:space="preserve">1. huius.</note>
            ſphæræ, maximus erit: </s>
            <s xml:id="echoid-s768" xml:space="preserve">qui circulum _A B,_ ſecet
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            in punctis _A, B,_ & </s>
            <s xml:id="echoid-s769" xml:space="preserve">iungatur ſemidiameter _D B,_
              <lb/>
            cui ex hypotheſi æqualis eſt _G D._ </s>
            <s xml:id="echoid-s770" xml:space="preserve">Quoniam vero
              <lb/>
            _C D,_ perpendicularis ponitur ad circulum A B,
              <lb/>
            erit, ex deſin. </s>
            <s xml:id="echoid-s771" xml:space="preserve">3. </s>
            <s xml:id="echoid-s772" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s773" xml:space="preserve">11. </s>
            <s xml:id="echoid-s774" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s775" xml:space="preserve">angulus _C D B,_ re-
              <lb/>
              <note position="right" xlink:label="note-033-06" xlink:href="note-033-06a" xml:space="preserve">Schol. 13.
                <lb/>
              fextf.</note>
            ctus. </s>
            <s xml:id="echoid-s776" xml:space="preserve">Quare _B D,_ media proportionalis eſt inter
              <lb/>
            _C D, D E,_ hoc eſt, erit, vt _C D,_ ad _B D,_ ita _B D,_
              <lb/>
            ad _D E._ </s>
            <s xml:id="echoid-s777" xml:space="preserve">Eſt autem _C D,_ ipſi _B D,_ æqualis. </s>
            <s xml:id="echoid-s778" xml:space="preserve">Igi-
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            tur & </s>
            <s xml:id="echoid-s779" xml:space="preserve">_D E,_ eidem _B D,_ æqualis erit; </s>
            <s xml:id="echoid-s780" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s781" xml:space="preserve">adeo
              <lb/>
            & </s>
            <s xml:id="echoid-s782" xml:space="preserve">_C D, D E,_ inter ſe æquales erunt. </s>
            <s xml:id="echoid-s783" xml:space="preserve">Cum ergo _C E,_ oſtenſa ſit tranſire per centrũ
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            ſphæræ, erit _D,_ centrum ſphæræ. </s>
            <s xml:id="echoid-s784" xml:space="preserve">Erat autem & </s>
            <s xml:id="echoid-s785" xml:space="preserve">centraum circuli _A B._ </s>
            <s xml:id="echoid-s786" xml:space="preserve">Idem ergo
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            eſt centrum ſphæræ. </s>
            <s xml:id="echoid-s787" xml:space="preserve">& </s>
            <s xml:id="echoid-s788" xml:space="preserve">circuli _A B,_ ac proinde circulus _A B,_ maximus eſt. </s>
            <s xml:id="echoid-s789" xml:space="preserve">Quod eſt
              <lb/>
              <note position="right" xlink:label="note-033-07" xlink:href="note-033-07a" xml:space="preserve">6. huius.</note>
            propoſitum.</s>
            <s xml:id="echoid-s790" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div90" type="section" level="1" n="53">
          <head xml:id="echoid-head64" xml:space="preserve">THEOREMA 15. PROPOS. 16.</head>
          <note position="right" xml:space="preserve">25.</note>
          <p>
            <s xml:id="echoid-s791" xml:space="preserve">SI in ſphæra ſit maximus circulus, recta linea
              <lb/>
            ducta ab eiuſdem circuli polo ad circunferentiã
              <lb/>
            æqualis eſt lateri quadrati inſcripti in maximo cir-
              <lb/>
            culo.</s>
            <s xml:id="echoid-s792" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s793" xml:space="preserve">IN ſphæra ſit circulus maximus A B, à cuius polo C, ad eius circũferentiã
              <lb/>
            ducatur recta C B. </s>
            <s xml:id="echoid-s794" xml:space="preserve">Dico C B, æqualẽ eſſe lateri quadrati in circulo A B, </s>
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